---
_id: '59171'
abstract:
- lang: eng
text: To model dynamical systems on networks with higher-order (non-pairwise) interactions,
we recently introduced a new class of ordinary differential equations (ODEs) on
hypernetworks. Here, we consider one-parameter synchrony breaking bifurcations
in such ODEs. We call a synchrony breaking steady-state branch ‘reluctant’ if
it is tangent to a synchrony space, but does not lie inside it. We prove that
reluctant synchrony breaking is ubiquitous in hypernetwork systems, by constructing
a large class of examples that support it. We also give an explicit formula for
the order of tangency to the synchrony space of a reluctant steady-state branch.
author:
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Eddie
full_name: Nijholt, Eddie
last_name: Nijholt
- first_name: Bob
full_name: Rink, Bob
last_name: Rink
citation:
ama: 'von der Gracht S, Nijholt E, Rink B. Higher-order interactions lead to ‘reluctant’
synchrony breaking. Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences. 2024;480(2301). doi:10.1098/rspa.2023.0945'
apa: 'von der Gracht, S., Nijholt, E., & Rink, B. (2024). Higher-order interactions
lead to ‘reluctant’ synchrony breaking. Proceedings of the Royal Society A:
Mathematical, Physical and Engineering Sciences, 480(2301). https://doi.org/10.1098/rspa.2023.0945'
bibtex: '@article{von der Gracht_Nijholt_Rink_2024, title={Higher-order interactions
lead to ‘reluctant’ synchrony breaking}, volume={480}, DOI={10.1098/rspa.2023.0945},
number={2301}, journal={Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences}, publisher={The Royal Society}, author={von der Gracht,
Sören and Nijholt, Eddie and Rink, Bob}, year={2024} }'
chicago: 'Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Higher-Order Interactions
Lead to ‘Reluctant’ Synchrony Breaking.” Proceedings of the Royal Society A:
Mathematical, Physical and Engineering Sciences 480, no. 2301 (2024). https://doi.org/10.1098/rspa.2023.0945.'
ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Higher-order interactions lead
to ‘reluctant’ synchrony breaking,” Proceedings of the Royal Society A: Mathematical,
Physical and Engineering Sciences, vol. 480, no. 2301, 2024, doi: 10.1098/rspa.2023.0945.'
mla: 'von der Gracht, Sören, et al. “Higher-Order Interactions Lead to ‘Reluctant’
Synchrony Breaking.” Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences, vol. 480, no. 2301, The Royal Society, 2024, doi:10.1098/rspa.2023.0945.'
short: 'S. von der Gracht, E. Nijholt, B. Rink, Proceedings of the Royal Society
A: Mathematical, Physical and Engineering Sciences 480 (2024).'
date_created: 2025-03-27T10:15:06Z
date_updated: 2025-03-27T10:19:56Z
ddc:
- '510'
department:
- _id: '101'
doi: 10.1098/rspa.2023.0945
file:
- access_level: open_access
content_type: application/pdf
creator: svdg
date_created: 2025-03-27T10:16:20Z
date_updated: 2025-03-27T10:19:48Z
file_id: '59172'
file_name: higher-order-interactions-lead-to-reluctant-synchrony-breaking.pdf
file_size: 820435
relation: main_file
file_date_updated: 2025-03-27T10:19:48Z
has_accepted_license: '1'
intvolume: ' 480'
issue: '2301'
keyword:
- higher-order interactions
- synchrony breaking
- network dynamics
- coupled cell systems
language:
- iso: eng
oa: '1'
publication: 'Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Sciences'
publication_identifier:
issn:
- 1364-5021
- 1471-2946
publication_status: published
publisher: The Royal Society
status: public
title: Higher-order interactions lead to ‘reluctant’ synchrony breaking
type: journal_article
user_id: '97359'
volume: 480
year: '2024'
...
---
_id: '16498'
author:
- first_name: P. J.
full_name: Aston, P. J.
last_name: Aston
- first_name: M.
full_name: Dellnitz, M.
last_name: Dellnitz
citation:
ama: 'Aston PJ, Dellnitz M. Computation of the dominant Lyapunov exponent via spatial
integration using matrix norms. Proceedings of the Royal Society of London
Series A: Mathematical, Physical and Engineering Sciences. 2003:2933-2955.
doi:10.1098/rspa.2003.1143'
apa: 'Aston, P. J., & Dellnitz, M. (2003). Computation of the dominant Lyapunov
exponent via spatial integration using matrix norms. Proceedings of the Royal
Society of London. Series A: Mathematical, Physical and Engineering Sciences,
2933–2955. https://doi.org/10.1098/rspa.2003.1143'
bibtex: '@article{Aston_Dellnitz_2003, title={Computation of the dominant Lyapunov
exponent via spatial integration using matrix norms}, DOI={10.1098/rspa.2003.1143},
journal={Proceedings of the Royal Society of London. Series A: Mathematical, Physical
and Engineering Sciences}, author={Aston, P. J. and Dellnitz, M.}, year={2003},
pages={2933–2955} }'
chicago: 'Aston, P. J., and M. Dellnitz. “Computation of the Dominant Lyapunov Exponent
via Spatial Integration Using Matrix Norms.” Proceedings of the Royal Society
of London. Series A: Mathematical, Physical and Engineering Sciences, 2003,
2933–55. https://doi.org/10.1098/rspa.2003.1143.'
ieee: 'P. J. Aston and M. Dellnitz, “Computation of the dominant Lyapunov exponent
via spatial integration using matrix norms,” Proceedings of the Royal Society
of London. Series A: Mathematical, Physical and Engineering Sciences, pp.
2933–2955, 2003.'
mla: 'Aston, P. J., and M. Dellnitz. “Computation of the Dominant Lyapunov Exponent
via Spatial Integration Using Matrix Norms.” Proceedings of the Royal Society
of London. Series A: Mathematical, Physical and Engineering Sciences, 2003,
pp. 2933–55, doi:10.1098/rspa.2003.1143.'
short: 'P.J. Aston, M. Dellnitz, Proceedings of the Royal Society of London. Series
A: Mathematical, Physical and Engineering Sciences (2003) 2933–2955.'
date_created: 2020-04-14T09:57:39Z
date_updated: 2022-01-06T06:52:51Z
department:
- _id: '101'
doi: 10.1098/rspa.2003.1143
language:
- iso: eng
page: 2933-2955
publication: 'Proceedings of the Royal Society of London. Series A: Mathematical,
Physical and Engineering Sciences'
publication_identifier:
issn:
- 1364-5021
- 1471-2946
publication_status: published
status: public
title: Computation of the dominant Lyapunov exponent via spatial integration using
matrix norms
type: journal_article
user_id: '47427'
year: '2003'
...